I want the device to save date and time for when the switch is on/off.
I'm not interested in measuring the level or strength or whatever of electricity.
I wonder how with such little knowledge you would even think of implementing this with an Arduino. A switch is a device intended for use with electricity.
So here is how it works:
Use a battery, your switch and a voltage data logger. All of these devices should have 2 connections:
Battery: positive and negative. Let's call them B+ and B-
Voltage logger: positive and negative (but does not matter since you are not interested in any values, only if the switch is on or off). Let's call them M+ and M-
Switch: 2 identical connections, let's call them S1 and S2.
Connect B- to M-
Connect B+ to S1
Connect S1 to M+
For gould measure you could add a 1M resistor between M+ and M- but this should be not necessary.
Once you have this setup completed the voltage meter should log 0V for switch open and the battery voltage for switch closed.